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A gradient-type method to solve a system of quadratic equations. (English) Zbl 0531.65026

Summary: Let us consider the following system of quadratic equations \[ \sum^{n}_{j=1}a_{i,j}x_ j+\sum^{n}_{j,k=1}b_{i,j,k}x_ jx_ k+c_ i=0,\quad i=1,...,m. \] This system arises in an inverse eigenvalue problem of mechanics. Numerical tests show that classical methods fail numerically even in cases n,\(m\leq 5\) in the solution of the above system. In this lecture we show a special gradient-type method to solve this system. Numerical examples are also considered.

MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C20 Quadratic programming
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